Welcome again!

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Martin Frimmer (mfrimmer@ethz.ch)Photonics LaboratoryHPP M24

• Check out the “Orientation sheet” on Moodle

Administrative details• 3 homework problems: find on Moodle, hand in on Moodle

• Dates for paper presentations fixed (please be available)

• Exams will take place in last week of semester (precise schedule to be published)

• You should have all necessary information to decide whether you want to follow this course. If you don’t want to get credit/take the exam, please sign out of the course by Tuesday, 29 Sep. (You are welcome to keep following the lectures and I can add you as a guest in case you want to access the Moodle.)

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Administrative details: Paper Presentations• I will assign the students I haven’t had feedback from

• I’ll share the schedule as soon as possible

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Today’s question

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Why do I not see the atoms that make up your skin when I look at you?

Maxwell’s equations for complex fields

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Spectral representation: For monochromatic fields:

Note that I dropped the underscore for complex fields!

The Helmholtz equation, plane and evanescent waves

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2. Dispersion relation:

1. Plane waves: 3. Speed of light:

4. Refractive index:

for

How do you generate evanescent waves?

Simple imaging systems

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On the menu today

• Motivation: Why nano-optics?

• Repetition: electromagnetism

• Optical imaging:• Focusing by a lens

• Angular spectrum• Paraxial approximation• Gaussian beams• Method of stationary phase

• The diffraction limit• Fluorophores• Example: Fluorescence microscopy• Example: STED microscopy• Example: Localization microscopy• Example: Scanning probe microscopy

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How does focusing by a lens work?

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Boundless.com

How does focusing by a lens work?

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x

k

θ1 = 0°

I(x) = E(x) E*(x) = ?

Intensity

How does focusing by a lens work?

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xI(x) = E(x) E*(x) = ?

θ1 = 20°

k

Intensity

How does focusing by a lens work?

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x

θ1 = ± 20°

k k

I(x) = E(x) E*(x) = ?

Intensity

How does focusing by a lens work?

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x

θ1 = ± 80°

k k

Intensity

How does focusing by a lens work?

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x

θ1 = 0°, ±45°

kkk

k

Intensity

How does focusing by a lens work?

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x

θ1 = 0°, ±15°, ±30°, ±45°, ±60°, ±75°

Intensity

How does focusing by a lens work?

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x

θ1 = 0°, ±15°, ±30°, ±45°, ±60°, ±75°

+apodization

Intensity

Angular spectrum

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MATH :

Angular spectrum

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MATH :

PHYS :

Angular spectrum

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MATH :

PHYS :

Together:

Angular spectrum

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PHYS :

Together:

Paraxial approximation

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mit

Fields propagate predominantly in z-direction !

Gaussian beams

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The Gaussian Beam

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Beam waist

Wavefront radius

Phase correction (Gouy phase)

Rayleigh length

Field in focal plane z=0:

The Gaussian Beam

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The Gaussian Beam has one free parameter. Which one?

The Gaussian Beam

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The Gaussian Beam has one free parameter. Which one?

The Gaussian Beam is an approximation!When is it a good approximation?

Does the Gaussian Beam contain evanescent field components?

Far-field

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s=

Example

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2 Lx

2 Ly

Example: Party-Party Goggles

Party-Party Goggles

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Party !

Party!Laser

Magic foil

500 µm

Party-Party

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Party !

Party!Laser

Magic foil

500 µm

FFT

SLM technology uses Fourier optics

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Party !

Party!Laser

Magic foil

Adaptive Version: Spatial light modulator (SLM)

A better description of focused fields

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Better than Gaussian beams, but not much to do analytically.